Notifications built into the OS (which all apps I've seen use other than Outlook and now Teams) are more functional and allow for more user control. Most importantly, they honor Do Not Disturb settings, which is critical.

Use Windows 10 notification center for notifications

The channel/team on which the notification has been made should stay more/better/longer visible so that you won't miss one.

Usual Microsoft lack of UI intuition.
Channels should be followed by default with the user unfollowing it if they wish.

It would be nice to let the Domain Admin have control what the default setting are in teams.
Users can changed them but let the admins change and override with one time Reset. Like a GPO Preference.

Why?
Let’s say the users are not ready for emails and Banners and users are freaking out about the number of Alerts from Teams to Outlook. The Admin could reset the setting for all users to Banner only. This would let users change it to email and banner, but the admin could find a setting that works best for the company of users.

I'm using Mac and one annoying thing is that I'm not getting notified of new messages in team channels (whether I'm mentioned or not) because I missed the banner in the top right of the screen, either from being away from my desk or focusing on my second screen. The red icon is added to the actual application icon in the dock menu when I get a direct chat but there should be something here to indicate that team chats have new messages

We need to get notifications based on keywords. For example: I am a subject matter expert for SAP and I like to know when SAP is typed into a channel so I can offer assistance.

Automatically mute all Teams notifications when on a video or audio conference call. Mute all notifications that are outside the conference call itself.

When a user in the Office 365 environment wants to use the web version http://teams.microsoft.com, a popup message is visible at the upper area with a prompt to install the client version:
“Want an even faster, more collaborative experience? Download the desktop app.” By several given security compliance requirements in big IT environments, the users shouldn’t be able to install any additional software at their PCs. This popup is confusing the web-only Teams user and also it makes the software deployment team nervous.

“Notification sounds = Off” will disable all sound notifications, including disabling the Call notifications. What I’d like to do is to disable Mention and Chat notification sounds for example, but keep Call notification sounds. This can't be done at the moment as only 3 options are available:
All
Call, mention and chat
Off
We would need additional options to cover all use cases.
Thanks

It would be really helpful to add more ways to notify teammates on through planner:
-Tag teammates in Planner Card comments
-Push notifications for mobile when mentioned in such tags.

Flashing taskbar notifications are a bit annoying, and it would be nice to have the option to turn off that flashing (while keeping popup notifications enabled).

Teams should respect Windows Focus Assist settings. I'm not even sure how apps are allowed to override Windows settings like this.
I put Windows Focus Assist into Alarms Only mode so I could record screen captures and I Teams kept popping up notifications over my application. I had to completely exit Teams so I could finish my task.

Not sure about the desktop clients because there isn't one available for my operating system. However, the web app is essentially unfit for purpose because I can't tell when anyone is trying to contact me unless I sit there, constantly staring at the app.

The sound you updated to during the week of March 6 is HORRIBLE. Please give us an option to change sounds for chat notifications the same way we can change sounds for the phone calls

Since everyone use the same ringtone, you sometimes do not know that your phone is the one ringing

When using Flow to post a message to a Team channel, the @mention does not trigger a notification. The text of the message is simply the "@mention" that was typed. Please enable a text recognition of @mention to enable the notification as though it were being typed directly in Teams.

Do Not Disturb should block all notifications and I'd love to be able to schedule DND, like on Slack